I'm going to play the optimist and for the sake of this exercise lets assume the device, with or without immediate major destruction to the planet, was in place and the smoke has finally settled.
Humans are now faced with the fact they are NOT alone in this universe. A realization that most, if not all, of their fundamental (geocentric) beliefs are shattered and will put aside their cultural hate / breed distaste mind set for each other to work as a single species and no longer as many nations.
If the artifact did major damage to the planet humans would most likely decide to quicken the pace to get off this mud hole and start to colonize at least our solar system.
An estimated price tag for an Earth elevator is 6 billion to 20 billion USD using a Nanotechnology that still needs improvements due to current length manufacturing limitations.
However the aliens just gave humanity a shortcut and since we no longer need the strength of a single nano-tech tether we can use existing tech such as nano-steel for platforms and tracks.
Seeing as we have the tech to build a Lunar elevator, bridging the gap between the two rocks would quickly follow.
What would a space elevator on the moon be made out of?
Were I a philanthropists leader of the liberated world, I would commission our best to fit super conductor train tracks and power transport by electromagnetism. Powered by the huge space array of solar panels or the nuclear power station bases located at a safe distance from orbit. Or perhaps the generators that use solar winds to function.
If the world politics stay the same for the most part and the philanthropists have difficulty with the politics surrounding land grab attempts of other nations it may be necessary to convince the majority of the world (the 99%) how unrestricted access to space will enrich and enlighten our species and increase our odds of survival.
If that doesn't work there is always the scare tactic that we need to be ready for when the aliens return and only we know how to defeat, defend, communicate, etc, with them.
With the resources our philanthropists have there is no doubt that a unifying message can be transmitted to the world and the people would rise and make a change. Perhaps a mass migration to join the philanthropists new nation leaving their countries of birth. Our philanthropists should have no remorse using their resources to build an army for the betterment of humankind. (Federation of Inner Sol Planets.)
If the event were destructive enough and perceived as an alien attack it wouldn't take much for an entity to manipulate the majority to unite under their flag for security.
The area around the space needle would no doubt become a hub of technological advancements and the center of any world power to which the philanthropists should be able to sway in their favor. Celebrity, Propaganda and Financial Resources go along way to building a political following!!!!